A350706 Composite numbers that have no "safe prime" factors.

4, 6, 8, 9, 12, 16, 18, 24, 26, 27, 32, 34, 36, 38, 39, 48, 51, 52, 54, 57, 58, 62, 64, 68, 72, 74, 76, 78, 81, 82, 86, 87, 93, 96, 102, 104, 106, 108, 111, 114, 116, 117, 122, 123, 124, 128, 129, 134, 136, 142, 144, 146, 148, 152, 153, 156, 158, 159, 162, 164, 169, 171

Offset

1,1

Comments

A350705 is a subsequence.

Links

Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Example

a(5) = 12 = 2 * 2 * 3 and {2, 3} are not in A005385.

Mathematica

Select[Range[200], CompositeQ[#] && AllTrue[FactorInteger[#][[;; , 1]], ! PrimeQ[(#1 - 1)/2] &] &] (* Amiram Eldar, Feb 20 2022 *)

Prog

(PARI) isok(m) = if ((m>1) && !isprime(m), !#select(x->isprime((x-1)\2), factor(m)[, 1]));
(Python)
from sympy import primefactors, isprime
print([n for n in range(4, 172) if not isprime(n) and all(not isprime((p-1)//2) for p in primefactors(n))])

Crossrefs

Cf. A350704, A350705, A005385.

Sequence in context: A028958 A200878 A344030 * A036310 A046760 A115684

Adjacent sequences: A350703 A350704 A350705 * A350707 A350708 A350709

Keyword

nonn

Author

Karl-Heinz Hofmann, Feb 20 2022

Status

approved